#include<iostream>
#include<unordered_map>
using namespace std;
const int MOD=1e9+7;


int main()
{
    int n; 
    cin >> n;
    unordered_map<int, int> prime;
    while(n--)
    {
        int x; cin >> x;

        for(int i = 2; i <= x / i; i++)
        {
            while(x % i == 0)
            {
                prime[i] ++;
                x = x / i;
            }
        }
        if(x > 1) prime[x]++;
    }
    

    long long ans=1;
    for(auto p:prime)
    {
        ans=ans*(p.second+1)%MOD;
    }
    cout<<ans;
    return 0;
}